[seqfan] Re: Knight's tour on infinite board

Hans Havermann gladhobo at bell.net
Sat May 4 20:17:51 CEST 2019

> It is dependant of course on the Ellermann spiral numbering scheme.

Ellermann's "Ulam spiral" variant goes north, then spirals clockwise. Every Ulam spiral I've looked at in a search just now goes east, then spirals counter-clockwise. The knight's tour sequences would of course be different superimposed on a "proper" Ulam spiral.

> The tour starts by filling in a central 5-by-5 square, starting in the square's center and ending in its SE corner. It then jumps 2 south and 1 east and proceeds to circle the 5-by-5 square clockwise four times filling in the now-9-by-9 square and ending in its SE corner. And so on.

If we flip the two-dimensional knight's tour over (in three-space) the spiral tour now runs counter-clockwise. Superimposed on Ellermann's Ulam spiral variant would generate new sequences differing from the eight that we have. So there is nothing really special about these eight sequences.

More information about the SeqFan mailing list